Enhanced single-node boundary condition for the Lattice Boltzmann Method

TL;DR

This paper introduces a novel single-node boundary condition method for the lattice Boltzmann method that achieves second-order accuracy and is effective for complex, moving, or immersed boundaries, improving upon existing techniques.

Contribution

The paper presents a new boundary condition implementation that uses data from only one node, providing higher accuracy and better suitability for complex and moving boundaries in lattice Boltzmann simulations.

Findings

Achieves second-order convergence for velocity fields.

Performs comparably or better than established boundary methods.

Effective for moving and immersed boundary simulations.

Abstract

We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well established Bouzidi, Firdaouss, and Lallemand (2001) boundary condition for curved walls, despite its local nature. The method also proves to be suitable to simulate moving rigid objects or immersed surfaces either with or without prescribed motion. The core idea of the new approach is to generalize the description of boundary conditions that combine bounce-back rule with interpolations and to enhance them by limiting the information involved in the interpolation to a close proximity of the boundary.